Abstract
Here we propose a new quantile density function estimator via block thresholding methods and investigate its asymptotic convergence rates under Lp risk with over Besov balls. We show that the considered estimator achieves optimal or near optimal rates of convergence according to the values of the parameter ν of the Besov classes
. We show that this estimator attain optimal and nearly optimal rates of convergence over a wide range of Besov function classes, and in particular enjoys those faster rates without the extraneous logarithmic penalties that given in Chesneau et al. A simulation study shows new proposed estimator performs better at the tails than existing competitors.